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A famous theorem of Gromov says that the set of compact Riemannian manifolds with $Ric \geq c$ and $\text{diam} \leq D$ is relatively compact in the Gromov-Hausdorff metric. Chapter 10 of the book by ...

There are two distinct notions in differential geometry associated with A. D. Alexandrov: (1) Alexandrov spaces of courvature bounded from below; (2) Alexandrov surfaces of bounded total curvature (...